INELASTIC Collisions m1v1before + m2v2before = (m1 + m2) vafter Elasticity 0% Inelastic Elastic More Data 5. What defines a collision as being inelastic? Only momentum is conserved and the kinetic energy is not conserved. 6. Simulate the four inelastic collisions below. Complete the table using math formulas and the simulation. BEFORE COLLISION AFTER COLLISION # m1 m2 V1 V2 Ptotal V1 and V2 1 2.0 kg 2.0 kg 1.5 m/s 0 3 kg " m/s .75 2 3.0 kg 6.0 kg 1.5 m/s -0.75 m/s 0 kg " m/s 0.0 3 1.5 kg 5.0 kg 2.0 m/s 0.2 m/s 4.03 kg " m/s .62 4 10.0 kg 10 kg 2.0 m/s -1.0 m/s 10.0 kg " m/s .5 7. Two objects moving toward each other with different momentums experience an inelastic collision. In which direction will both objects travel after the collision? Both objects will travel in the direction of the body having larger initial momentum 8. A less-massive object is moving in the same direction as a more-massive object, but with a higher speed. They experience an inelastic collision. Describe the speed of the more-massive object after the collision. 9. Objects 1 has half the mass of object 2 and the objects move toward each other and experience an inelastic collision. If both objects do not move after the collision compare the velocity of both objects before the collision. If the less massive object has two times the velocity and half the mass the two will not move in any direction. 10. Show mathematically the total momentum before the collision in trial #1 is conserved after the collision. Initial momentum before collision = m1V1 + m2V2 = Final momentum after collision m1V1 + m2V2 =
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0 kg$, $v_{1i} = 1.5 m/s$, $m_2 = 2.0 kg$, and $v_{2i} = 0 m/s$. $p_i = (2.0 kg)(1.5 m/s) + (2.0 kg)(0 m/s) = 3.0 kg m/s$ Show moreā¦
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Suppose the two cars had rubber bumpers in the front and back ā similar to the bumper cars children (of all ages!) ride at amusement parks. Also, suppose that the cars are sturdy enough that the metal they are made of does not bend during the collision. In this case, the cars would undergo a perfectly elastic collision. Assume, just like in the first collision question, that the SUV (initially moving to the right) collides into the stationary smart car. After the collision, the smart car will obviously move to the right. What about the SUV? (Hint: What do you think would happen if the SUV was much larger than the smart car, e.g., has a mass that is 50 times larger?) The SUV will move to the right. After the collision, which car do you think moves faster? Why? The smart car because it has less mass. Since this is a collision, momentum is conserved. Write down the momentum conservation equation for this situation. Mass of smart car = 1000 kg, mass of SUV = 4000 kg, initial speed of SUV = 15 m/s. 4v1 + v2 = 60 Is this equation sufficient to find the speeds of the two cars after the collision? Why or why not? No because it includes two variables and we still need to find the speed after the collision. What other quantity is conserved during a perfectly elastic collision? Write down the equation for that conservation. 1/2m1u1^2 + 1/2m2u2^2 = 1/2m1v1^2 + 1/2m2v2^2 If you have not done so already, simplify the two equations (e.g., by dividing by 1000) and rewrite them here. If you have simplified them, just rewrite them here. 4v1 + v2 = 60 4v1^2 + v2^2 = 900 A. Using these two equations, it is possible to solve for both final speeds. However, the algebra is somewhat challenging because one of the equations has the final speeds of the two cars both squared. The book provides the general solutions to these equations in which you can plug in the initial speeds and the masses of the cars and obtain the final speeds. That wonāt be necessary here. Instead, suppose someone measures the final speed of the SUV to be 9.0 m/s. What is the final speed of the smart car? You should get the same number if you use either equation, so make sure you use both. Using the momentum equation: Using the conservation of KE equation: B. Suppose that this collision also took 0.1 seconds. What is the magnitude of the net force acting on either car during the collision? How does this force compare to the perfectly inelastic collision? What is the acceleration acting on the smart car? On the SUV? C. Generally, how do elastic collisions compare to perfectly inelastic collisions? Discuss the forces being exerted on the cars, the accelerations, and the kinetic energies.
Hafiz S.
Learning Goal: To understand how to find the velocities of objects after a collision. There are two main types of collisions that you will study: perfectly elastic collisions and perfectly inelastic collisions. When two objects collide elastically, both total kinetic energy and total momentum are conserved. These two conservation laws allow the final motion of the two objects to be determined. When two objects collide inelastically, total momentum is conserved, but the total kinetic energy is not conserved. After an inelastic collision, the two objects are stuck together, and thus travel with the same final velocity. This fact, together with conservation of momentum, allows the final motion of the two objects to be calculated. In reality, there is a range of collision types, with elastic and perfectly inelastic at the extreme ends. These extreme cases allow for a more straightforward analysis than the in-between cases. The video at the end of the problem will give you a chance to explore the "in-between" collisions. Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary. Part A: If the collision is perfectly elastic, what are the final velocities v1 and v2 of objects 1 and 2? Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express each velocity in terms of v. Part B: Now suppose that the collision is perfectly inelastic. What are the velocities v1 and v2 of the two objects after the collision? Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express the velocities in terms of v. Part C: Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of objects 1 and 2? Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express the velocities in terms of v. Part D: Let the mass of object 1 be m and the mass of object 2 be 3m. If the collision is perfectly inelastic, what are the velocities of the two objects after the collision? Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express the velocities in terms of v.
Josee P.
Part 1 (a) First we consider the interaction of two objects, one of mass m1 and the other of mass m2, where m1 > m2. The two objects are moving with the same speed v toward each other. After they collide the object of mass m1 has its same speed but is moving at an angle Īø relative to its initial velocity. Draw a picture showing the momentum before the collision and the momentum after the collision. Include an appropriate x-y coordinate axis. Make sure your momentum vectors have appropriate sizes as well as direction. (b) Find the components of the final velocity of the object of mass m2. (c) Find the components of the impulse delivered to the object of mass m1, and then the components of the impulse delivered to the object of mass m2 during the collision. How are these two impulses related? (d) Is the force on the object of mass m1 equal to, greater than, or less than the force exerted on the object of mass m2? Explain. Part 2 (a) Now consider an explosion where the initial object is at rest and explodes into three pieces of different masses m1 < m2 < m3. After the explosion the first two masses move with the same speed v but with velocities separated by 60 degrees. Draw a picture showing the momenta of the three pieces after the collision. Include an appropriate x-y coordinate system. 2 (b) Find the x- and y-coordinates of the velocity of the third piece of mass m3. Evaluate any trig functions in your answers.
Sri K.
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